Finite Group Databasebeta

← C2×#24918589 #36276443

Subgroups — C2×#24918589 #36276443

Order 21248.

2286 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128246C211yesmaximal, characteristic
2C22×#14581791C211yesmaximal, characteristic, complemented
3#24918589C2116yesmaximal, direct product factor
4C2×#19128098C212yesmaximal, complemented
5C2×#19128046C212yesmaximal, complemented
6C2×#19128020C211yesmaximal, characteristic, complemented
7C2×#19128019C211yesmaximal, characteristic, complemented
8C2×#19128017C211yesmaximal, characteristic, complemented
9C2×#19127990C212yesmaximal, complemented
10C2×#19127989C212yesmaximal, complemented
11C2×#19127751C211yesmaximal, characteristic, complemented
12C2×#481×C83C211yesmaximal, characteristic, complemented
13C22×#13050589—21no—
14C23×Dic166—21no—
15#19128246—24no—
16#19128246C2218yes—
17C2×#14581791—24no—
18C2×#14581791—21no—
19C2×#14581791—21no—
20C2×#14581791C2212yes—
21C2×#14581791C2212yes—
22C2×#14581791C2211yescharacteristic
23C2×#14581791C2218yescomplemented
24C2×#14581788C2211yescharacteristic
25C2×#14581778—21no—
26C2×#14581766C2211yescharacteristic
27C2×#14581764—21no—
28C2×D4×Dic83C2211yescharacteristic
29C2×#14581754C2211yescharacteristic
30C2×(C22⋊D83)⋊C4—21no—
31C22×C4⋊Dic83C2211yescharacteristic
32C22×Dic83⋊C4—21no—
33C22×C4×Dic83C2211yescharacteristic
34#19128098C22116yescomplemented
35#19128046C22116yescomplemented
36#19128020C2218yescomplemented
37#19128019C2218yescomplemented
38#19128017C2218yescomplemented
39#19127990C22116yescomplemented
40#19127989C22116yescomplemented
41#19127751C2218yescomplemented
42C2×#14581724C2212yes—
43C2×#14581723C2212yes—
44C2×#14581723C2212yes—
45C2×Dic83⋊C8C2212yes—
46C2×#14581714C2212yes—
47C2×#14581713C2212yes—
48C2×#14581712C2212yes—
49C2×C22⋊(C83⋊C8)C2211yescharacteristic
50C2×C8×Dic83C2212yes—
51C2×#121×C83C2211yescharacteristic
52C22×C4⋊C4×C83C2211yescharacteristic
53#481×C83C2218yescomplemented
54C2×#106×C83C2212yes—
55C2×#102×C83C2212yes—
56C2×C22⋊C8×C83C2211yescharacteristic
57C2×#13050589—28no—
58C2×#13050589—48no—
59C22×Dic166—21no—
60C22×Dic166—22no—
61C22×Dic166—22no—
62C22×Dic166—28no—
63C22×Dic166—48no—
64C22×D332C2311yescharacteristic
65C22×C22⋊D83—21no—
66C22×C22⋊D83—21no—
67C22×C22⋊D83—21no—
68C23×Dic83—21no—
69C23×Dic83—21no—
70C23×Dic83D411yescharacteristic
71C23×Dic83D411yescharacteristic
72C22×C4×D83—21no—
73C22×C83⋊C8C2312yes—
74#14581791—24no—
75#14581791—24no—
76#14581791—28no—
77#14581791—28no—
78#14581791—22no—
79#14581791C2314yes—
80#14581791C2318yes—
81#14581791C2318yes—
82#14581788—22no—
83#14581788C2314yes—
84#14581778—28no—
85#14581766—22no—
86#14581766C2314yes—
87#14581764—28no—
88D4×Dic83—22no—
89D4×Dic83C2314yes—
90#14581754—22no—
91#14581754C2314yes—
92(C22⋊D83)⋊C4—28no—
93C2×C4⋊Dic83—22no—
94C2×C4⋊Dic83—21no—
95C2×C4⋊Dic83C2312yes—
96C2×C4⋊Dic83C2314yes—
97C2×C4⋊Dic83C2311yescharacteristic
98C2×Dic83⋊C4—22no—
99C2×Dic83⋊C4—22no—
100C2×Dic83⋊C4—28no—
101C2×Dic83⋊C4—21no—
102C2×C22⋊Dic83—21no—
103C2×(C2×D83)⋊C4—21no—
104C2×(C2×D83)⋊C4—21no—
105C2×C4×Dic83D411yescharacteristic
106C2×C4×Dic83D411yescharacteristic
107C2×C4×Dic83D414yes—
108C2×C4×Dic83C2311yescharacteristic
109C2×C4×Dic83C2311yescharacteristic
110C2×C4×Dic83C2314yes—
111#14581724C2318yes—
112#14581723C2318yes—
113#14581723C2318yes—
114Dic83⋊C8C2318yes—
115#14581714C2318yes—
116#14581713C2318yes—
117#14581712C2318yes—
118C22⋊(C83⋊C8)C2314yes—
119C8×Dic83C2318yes—
120C22×D4×C83—21no—
121C22×D4×C83C2311yescharacteristic
122C23×C4×C83—21no—
123C23×C4×C83C2311yescharacteristic
124C22×C8×C83C2312yes—
125#121×C83—22no—
126#121×C83C2314yes—
127C2×C4⋊C4×C83—22no—
128C2×C4⋊C4×C83—21no—
129C2×C4⋊C4×C83C2314yes—
130C2×C4⋊C4×C83C2312yes—
131C2×C4⋊C4×C83C2311yescharacteristic
132C2×C22⋊C4×C83—21no—
133#106×C83C2318yes—
134#102×C83C2318yes—
135C22⋊C8×C83C2314yes—
136C23×D83—21no—
137#13050589—432no—
138C2×Dic166—24no—
139C2×Dic166—28no—
140C2×Dic166—28no—
141C2×Dic166—48no—
142C2×Dic166—432no—
143C2×Dic166—44no—
144C2×Dic166—48no—
145C2×D332—24no—
146C2×D332—21no—
147C2×D332C2412yes—
148C2×C22⋊D83—24no—
149C2×C22⋊D83—24no—
150C2×C22⋊D83—24no—
151C2×C22⋊D83—44no—
152C2×C22⋊D83—44no—
153C2×C22⋊D83—44no—
154C22×Dic83—24no—
155C22×Dic83—21no—
156C22×Dic83—24no—
157C22×Dic83—22no—
158C22×Dic83—24no—
159C22×Dic83—44no—
160C22×Dic83—44no—
161C22×Dic83SD1618yes—
162C22×Dic83C2×D414yes—
163C22×Dic83C2×D411yescharacteristic
164C22×Dic83C2×D411yescharacteristic
165C22×Dic83C2×D411yescharacteristic
166C22×Dic83C2×D414yes—
167C22×Dic83C2×D411yescharacteristic
168C2×C4×D83—24no—
169C2×C4×D83—44no—
170C2×C83⋊C8—24no—
171C2×C83⋊C8C2414yes—
172C4⋊Dic83—21no—
173C4⋊Dic83—24no—
174C4⋊Dic83—22no—
175C4⋊Dic83C2412yes—
176C4⋊Dic83C2414yes—
177Dic83⋊C4—24no—
178Dic83⋊C4—28no—
179Dic83⋊C4—28no—
180C22⋊Dic83—24no—
181(C2×D83)⋊C4—24no—
182(C2×D83)⋊C4—24no—
183C4×Dic83C2×D414yes—
184C4×Dic83C2×D412yes—
185C4×Dic83C2×D414yes—
186C4×Dic83C2×D412yes—
187C4×Dic83C2412yes—
188C4×Dic83C2412yes—
189C24×C83—21no—
190C24×C83C2×D411yescharacteristic
191C2×D4×C83—24no—
192C2×D4×C83—21no—
193C2×D4×C83—24no—
194C2×D4×C83—44no—
195C2×D4×C83C2412yes—
196C22×C4×C83—24no—
197C22×C4×C83—21no—
198C22×C4×C83—24no—
199C22×C4×C83—22no—
200C22×C4×C83—44no—
201C22×C4×C83C2×D412yes—
202C22×C4×C83C2×D411yescharacteristic
203C22×C4×C83C2412yes—
204C22×C4×C83C2411yescharacteristic
205C2×C8×C83—24no—
206C2×C8×C83C2414yes—
207C4⋊C4×C83—24no—
208C4⋊C4×C83—22no—
209C4⋊C4×C83—21no—
210C4⋊C4×C83C2414yes—
211C4⋊C4×C83C2412yes—
212C22⋊C4×C83—24no—
213C23×C83—22no—
214C23×C83—22no—
215C23×C83—22no—
216C23×C83—42no—
217C23×C83—42no—
218C23×C83—42no—
219C23×C83C2×SD1614yes—
220C23×C83C22×D412yes—
221C23×C83C22×D411yescharacteristic
222C22×D83—22no—
223C22×D83—42no—
224C22×D83—42no—
225C22×D83—42no—
226D4×C83—24no—
227D4×C83—48no—
228D4×C83—42no—
229C2×C4×C83—22no—
230C2×C4×C83—24no—
231C2×C4×C83—24no—
232C2×C4×C83—22no—
233C2×C4×C83—24no—
234C2×C4×C83—48no—
235C2×C4×C83—42no—
236C2×C4×C83—44no—
237C2×C4×C83C22×D412yes—
238C2×C4×C83C22×D411yescharacteristic
239C2×C4×C832−1+414yes—
240C2×C4×C83C2511yescharacteristic
241C22⋊D83—48no—
242C22⋊D83—48no—
243C22⋊D83—48no—
244C2×Dic83—22no—
245C2×Dic83—28no—
246C2×Dic83—22no—
247C2×Dic83—24no—
248C2×Dic83—48no—
249C2×Dic83—42no—
250C2×Dic83—44no—
251C2×Dic83—48no—
252C2×Dic83C2×SD1614yes—
253C2×Dic83C2×SD1614yes—
254C2×Dic83C2×SD16116yes—
255C2×Dic83AGL(1,ℤ/8)14yes—
256C2×Dic83C22×D412yes—
257C2×Dic83C22×D412yes—
258C2×Dic83C22×D412yes—
259C2×Dic83C22×D412yes—
260D332—24no—
261D332—42no—
262C4×D83—48no—
263Dic166—416no—
264Dic166—48no—
265Dic166—416no—
266C8×C83—24no—
267C83⋊C8—24no—
268C22×C83—22no—
269C22×C83—28no—
270C22×C83—22no—
271C22×C83—42no—
272C22×C83—42no—
273C22×C83—42no—
274C22×C83—84no—
275C22×C83#53612yes—
276C22×C83C22×SD1614yes—
277C22×C83C22×SD1612yes—
278C22×C83C2×AGL(1,ℤ/8)12yes—
279C22×C83C23×D411yescharacteristic
280C2×D83—42no—
281C2×D83—42no—
282C2×D83—42no—
283C2×D83—84no—
284C4×C83—22no—
285C4×C83—42no—
286C4×C83—44no—
287C4×C83#53612yes—
288C4×C83C2×2−1+412yes—
289Dic83—22no—
290Dic83—42no—
291Dic83—44no—
292Dic83C22×SD1614yes—
293Dic83C22×SD1614yes—
294Dic83C2×AGL(1,ℤ/8)14yes—
295C2×#3227—831nomaximal, Sylow
296C2×C83—24no—
297C2×C83—82no—
298C2×C83#322714yescomplemented
299C2×C83C2×#53611yescharacteristic
300C2×C83C23×SD1611yescharacteristic
301C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
302D83—82no—
303C2×#532—831no—
304C22×C4⋊Q8—831no—
305#3227—8316no—
306C2×#498—832no—
307C2×#486—832no—
308C2×#481—831no—
309C2×#481—831no—
310C2×#481—831no—
311C2×#481D8311yescharacteristic, complemented
312C2×#476—832no—
313C2×#476—832no—
314C2×#431—831no—
315C83C2×#322711yescharacteristic, complemented, Sylow
316C22×#41—1661no—
317C23×Q8—1661no—
318#532—838no—
319#532—1664no—
320C2×C4⋊Q8—832no—
321C2×C4⋊Q8—831no—
322C2×C4⋊Q8—838no—
323C2×C4⋊Q8—832no—
324C2×C4⋊Q8—1661no—
325C2×C4⋊Q8—1661no—
326C2×C4⋊Q8—1664no—
327C2×#127—831no—
328C2×#124—1661no—
329C2×#121—831no—
330C2×#121—1661no—
331C2×#121C2×D8311yescharacteristic
332C2×C4×D4—831no—
333C2×C4×D4—831no—
334C2×C4×D4—1661no—
335C22×C4⋊C4—831no—
336C22×C4⋊C4—1661no—
337C22×C4⋊C4C2×D8311yescharacteristic
338C22×C42—831no—
339#498—8316no—
340#486—8316no—
341#481—838no—
342#481—838no—
343#481—838no—
344#481C2×D8318yescomplemented
345#476—8316no—
346#476—8316no—
347#431—838no—
348C2×#106—832no—
349C2×#106—832no—
350C2×#106—832no—
351C2×#106C2×D8312yes—
352C2×C4⋊C8—832no—
353C2×#102—832no—
354C2×#102—832no—
355C2×#102—832no—
356C2×#102C2×D8312yes—
357C2×C22⋊C8—831no—
358C2×C22⋊C8C2×D8311yescharacteristic
359C2×C4×C8—832no—
360C2×#41—3328no—
361C2×#41—1668no—
362C22×Q8—3328no—
363C22×Q8—1661no—
364C22×Q8—1668no—
365C22×Q8—1662no—
366C22×Q8—1662no—
367C22×D4—21no—
368C22×D4—831no—
369C22×D4—1661no—
370C22×D4—1661no—
371C22×D4—1661no—
372C22×D4C22×D8311yescharacteristic
373C23×C4—21no—
374C23×C4—831no—
375C23×C4—831no—
376C23×C4—1661no—
377C23×C4—1661no—
378C23×C4—1661no—
379C23×C4C22×D8311yescharacteristic
380C22×C8—832no—
381C22×C8C22×D8312yes—
382C4⋊Q8—838no—
383C4⋊Q8—838no—
384C4⋊Q8—834no—
385C4⋊Q8—1668no—
386C4⋊Q8—1664no—
387C4⋊Q8—1668no—
388C4⋊Q8—1664no—
389C4⋊Q8—1662no—
390#127—834no—
391#127—1662no—
392#124—1668no—
393#121—22no—
394#121—834no—
395#121—1668no—
396#121—1662no—
397#121C22×D8314yes—
398C4×D4—834no—
399C4×D4—834no—
400C4×D4—1668no—
401C4×D4—1662no—
402C4×D4—1662no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—832no—
406C2×C4⋊C4—834no—
407C2×C4⋊C4—831no—
408C2×C4⋊C4—1668no—
409C2×C4⋊C4—1662no—
410C2×C4⋊C4—1662no—
411C2×C4⋊C4—1661no—
412C2×C4⋊C4—1662no—
413C2×C4⋊C4—1661no—
414C2×C4⋊C4C22×D8312yes—
415C2×C4⋊C4C22×D8314yes—
416C2×C4⋊C4C22×D8311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—1661no—
419C2×C22⋊C4—1661no—
420C2×C22⋊C4—1661no—
421C2×C42—831no—
422C2×C42—831no—
423C2×C42—834no—
424C2×C42—831no—
425C2×C42—831no—
426C2×C42—834no—
427#106—838no—
428#106—838no—
429#106—838no—
430#106C22×D8318yes—
431C4⋊C8—838no—
432#102—838no—
433#102—838no—
434#102—838no—
435#102C22×D8318yes—
436C22⋊C8—834no—
437C22⋊C8C22×D8314yes—
438C4×C8—838no—
439C24—21no—
440C24—1661no—
441C24D4×D8311yescharacteristic
442#41—33232no—
443C2×Q8—3328no—
444C2×Q8—3324no—
445C2×Q8—33232no—
446C2×Q8—3328no—
447C2×Q8—1664no—
448C2×Q8—1668no—
449C2×Q8—1668no—
450C2×D4—24no—
451C2×D4—21no—
452C2×D4—24no—
453C2×D4—44no—
454C2×D4—3324no—
455C2×D4—3324no—
456C2×D4—3324no—
457C2×D4—832no—
458C2×D4—1664no—
459C2×D4—1664no—
460C2×D4—1664no—
461C2×D4—1661no—
462C2×D4—1664no—
463C2×D4C23×D8312yes—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—44no—
469C22×C4—3324no—
470C22×C4—3324no—
471C22×C4—3324no—
472C22×C4—838no—
473C22×C4—834no—
474C22×C4—831no—
475C22×C4—831no—
476C22×C4—831no—
477C22×C4—834no—
478C22×C4—831no—
479C22×C4—1664no—
480C22×C4—1664no—
481C22×C4—1664no—
482C22×C4—1661no—
483C22×C4—1662no—
484C22×C4—1664no—
485C22×C4D4×D8312yes—
486C22×C4D4×D8311yescharacteristic
487C22×C4C23×D8312yes—
488C22×C4C23×D8311yescharacteristic
489C2×C8—24no—
490C2×C8—834no—
491C2×C8—1664no—
492C2×C8C23×D8314yes—
493C4⋊C4—24no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—834no—
497C4⋊C4—832no—
498C4⋊C4—1668no—
499C4⋊C4—1668no—
500C4⋊C4—1664no—
501C4⋊C4—1664no—
502C4⋊C4—1662no—
503C4⋊C4—1661no—
504C4⋊C4C23×D8314yes—
505C4⋊C4C23×D8312yes—
506C22⋊C4—24no—
507C22⋊C4—1664no—
508C22⋊C4—1664no—
509C22⋊C4—1664no—
510C42—834no—
511C42—832no—
512C42—834no—
513C42—832no—
514C42—832no—
515C42—832no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—3322no—
523C23—3322no—
524C23—3322no—
525C23—1662no—
526C23SD16×D8314yes—
527C23C2×D4×D8312yes—
528C23C2×D4×D8311yescharacteristic
529Q8—33216no—
530Q8—3328no—
531Q8—33216no—
532D4—24no—
533D4—48no—
534D4—42no—
535D4—3328no—
536D4—3328no—
537D4—3328no—
538D4—3322no—
539D4—1664no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—48no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—3328no—
549C2×C4—3328no—
550C2×C4—3322no—
551C2×C4—3324no—
552C2×C4—3328no—
553C2×C4—834no—
554C2×C4—834no—
555C2×C4—8316no—
556C2×C4—834no—
557C2×C4—832no—
558C2×C4—832no—
559C2×C4—832no—
560C2×C4—832no—
561C2×C4—1662no—
562C2×C4—1664no—
563C2×C4—1668no—
564C2×C4—1662no—
565C2×C4C2×D4×D8312yes—
566C2×C4C2×D4×D8311yescharacteristic
567C2×C4#1458183914yes—
568C2×C4C24×D8311yescharacteristic
569C8—24no—
570C8—1664no—
571C22—28no—
572C22—22no—
573C22—22no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—84no—
578C22—3322no—
579C22—3322no—
580C22—3322no—
581C22—6644no—
582C22#1912827312yes—
583C22C2×SD16×D8314yes—
584C22C2×SD16×D8312yes—
585C22AGL(1,ℤ/8)×D8312yes—
586C22C22×D4×D8311yescharacteristic
587C4—22no—
588C4—42no—
589C4—44no—
590C4—3322no—
591C4—3324no—
592C4—834no—
593C4—834no—
594C4—834no—
595C4—1662no—
596C4#1912827312yes—
597C4C2×#1458183912yes—
598C2—24no—
599C2—82no—
600C2—6642no—
601C2#2491858914yesdirect product factor
602C2C2×#1912827311yescharacteristic
603C2C22×SD16×D8311yescharacteristic
604C2C2×AGL(1,ℤ/8)×D8311yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#481×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128246C2
hypercenterC2×#481D83
hypocenterC83C2×#3227
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×#14581791C2semidirect
3. #24918589C2direct (N × H)
4. C2×#19128098C2semidirect
5. C2×#19128046C2semidirect
6. C2×#19128020C2semidirect
7. C2×#19128019C2semidirect
8. C2×#19128017C2semidirect
9. C2×#19127990C2semidirect
10. C2×#19127989C2semidirect
11. C2×#19127751C2semidirect
12. C2×#481×C83C2semidirect
23. C2×#14581791C22semidirect
34. #19128098C22semidirect
35. #19128046C22semidirect
36. #19128020C22semidirect
37. #19128019C22semidirect
38. #19128017C22semidirect
39. #19127990C22semidirect
40. #19127989C22semidirect
41. #19127751C22semidirect
53. #481×C83C22semidirect
298. C2×C83#3227semidirect
311. C2×#481D83semidirect
315. C83C2×#3227semidirect
344. #481C2×D83semidirect
601. C2#24918589direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191282462
C22×#145817912
#249185892
C2×#191280982
C2×#191280462
C2×#191280202
C2×#191280192
C2×#191280172
C2×#191279902
C2×#191279892
C2×#191277512
C2×#481×C832
C2×#322783